Electrophoretic motion of spherical particles with a nonuniform charge distribution

Abstract

The electrophoretic motion of a non-Brownian rigid sphere with an arbitrary particle charge distribution is studied. Utilizing the multipole expansion of the double-layer potential based on the linearized Poisson-Boltzmann equation, the electrophoretic motion is analyzed for a sphere with an arbitrary double-layer thickness. Only the monopole and quadrupole moments can contribute to the translational motion of the sphere, while only the dipole moment can result in rotational motion. Furthermore, the monopole moment contribution to the electrophoretic mobility exactly follows the classical expression of Henry. Simple relationships are derived for the multipole moments of the surface potential and the multipole moments of the particle charge distribution so that electrophoretic mobility data can be interpreted in terms of either set of moments.